# Great disnub cube

Great disnub cube Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGidsac
Elements
Components6 square antiprisms
Faces48 triangles, 12 squares as 6 stellated octagons
Edges48+48
Vertices48
Vertex figureIsosceles trapezoid, edge length 1, 1, 1, 2
Measures (edge length 1)
Circumradius$\sqrt{\frac{4+\sqrt2}{8}} \approx 0.82267$ Volume$2\sqrt{4+3\sqrt2} \approx 5.74200$ Dihedral angles3–3: $\arccos\left(\frac{1-2\sqrt2}{3}\right) \approx 127.55160^\circ$ 4–3: $\arccos\left(\frac{\sqrt3-\sqrt6}{3}\right) \approx 103.83616^\circ$ Central density6
Number of external pieces336
Level of complexity52
Related polytopes
ArmySemi-uniform Girco
RegimentGidsac
DualCompound of six square antitegums
ConjugateGreat disnub cube
Abstract & topological properties
Flag count384
OrientableYes
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

The great disnub cube, gidsac, or compound of six square antiprisms is a uniform polyhedron compound. It consists of 48 triangles and 12 squares (which pair up into 6 stellated octagons due to lying in the same plane), with one square and three triangles joining at a vertex.

It can be formed by combining the two chiral forms of the great snub cube.

Its quotient prismatic equivalent is the square antiprismatic hexateroorthowedge, which is eight-dimensional.

## Vertex coordinates

The vertices of a great disnub cube of edge length 1 are given by all permutations of:

• $\left(\pm\sqrt{\frac{2+\sqrt2}{8}},\,\pm\sqrt{\frac{2-\sqrt2}{8}},\,\pm\frac{\sqrt{8}}{4}\right).$ 